TwistKnot

The twist knot with $n$ half-twists past its clasp, for nonzero integer $n$ — $n=1$ is the figure-eight and $n=-1$ is the trefoil.

TwistKnot(n)the twist knot with $n$ half-twists past its clasp

Typed signatures

Type	Package	Applies
(integer) -> expression<TwistKnot>	braid	always

Domain: Braids and knots

Examples

Basic #

The $5_2$ knot

live ↗

In$\mathrm{AlexanderPolynomial}(\mathrm{TwistKnot}(2))$Out$2t^2-5t+2$

Matches the trefoil's bracket

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In$\mathrm{BracketInvariant}(\mathrm{TwistKnot}(-1))$Out$-\frac{1}{A^{16}}+\frac{1}{A^{12}}+\frac{1}{A^4}$

About

Examples	2

See also: FigureEightKnot, PretzelKnot, AlexanderPolynomial